This invention relates to a packing for installation in columns or pipes through which a fluid flows with the purpose of exchange of material. The main technical fields of application are: rectification, absorption, mixing, heat transfer and deposition of particles and droplets. The packing described here consists of a plurality of twisted strips layered parallel to each other in an axially symmetric arrangement. Such inserts for apparatus have been disclosed in French Pat. No. 2 301 281 and published European Application No. 0 011 176. Although these devices have been found to be quite satisfactory in practice, they have the disadvantage of relatively low mechanical stability when manufactured from fabric. Such a packing is readily deformed when installed or removed and thereby damaged. The damage produced is frequently not externally recognizable and only discovered by the substantially reduced efficiency in operation. In known packings, the individual elements, i.e. the twisted strips (spirals) are either mechanically connected by webs, bands or wires, or directly soldered or welded together at the point of contact of the strips. Such connections require a complicated and therefore expensive manufacturing technique.